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Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values
and eigen vectors.
Calculus: Mean value theorems, Theorems of integral calculus,
Evaluation of definite and improper integrals, Partial Derivatives, Maxima
and minima, Multiple integrals, Fourier series. Vector identities,
Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss
and Green's theorems.
Differential equations: First order equation (linear and nonlinear),
Higher order linear differential equations with constant coefficients, Method
of variation of parameters, Cauchy's and Euler's equations, Initial and boundary
value problems, Partial Differential Equations and variable separable method.
Complex variables: Analytic functions, Cauchy's integral theorem and
integral formula, Taylor's and Laurent' series, Residue theorem, solution
integrals.
Probability and Statistics: Sampling theorems, Conditional
probability, Mean, median, mode and standard deviation, Random variables,
Discrete and continuous distributions, Poisson, Normal and Binomial
distribution, Correlation and regression analysis.
Numerical Methods: Solutions of non-linear algebraic equations, single
and multi-step methods for differential equations.
Transform Theory: Fourier transform, Laplace transform, Z-transform.
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Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis,
transient response of dc and ac networks; sinusoidal steady-state analysis,
resonance, basic filter concepts; ideal current and voltage sources,
Thevenin's, Norton's and Superposition and Maximum Power Transfer theorems,
two-port networks, three phase circuits; Gauss Theorem, electric field and
potential due to point, line, plane and spherical charge distributions;
Ampere's and Biot-Savart's laws; inductance; dielectrics; capacitance.
Signals and Systems: Representation of continuous and discrete-time
signals; shifting and scaling operations; linear, time-invariant and causal
systems; Fourier series representation of continuous periodic signals;
sampling theorem; Fourier, Laplace and Z transforms.
Electrical Machines: Single phase transformer - equivalent circuit,
phasor diagram, tests, regulation and efficiency; three phase transformers -
connections, parallel operation; auto-transformer; energy conversion
principles; DC machines - types, windings, generator characteristics,
armature reaction and commutation, starting and speed control of motors;
three phase induction motors - principles, types, performance
characteristics, starting and speed control; single phase induction motors;
synchronous machines - performance, regulation and parallel operation of
generators, motor starting, characteristics and applications; servo and
stepper motors.
Power Systems: Basic power generation concepts; transmission line
models and performance; cable performance, insulation; corona and radio
interference; distribution systems; per-unit quantities; bus impedance and
admittance matrices; load flow; voltage control; power factor correction;
economic operation; symmetrical components; fault analysis; principles of
over-current, differential and distance protection; solid state relays and
digital protection; circuit breakers; system stability concepts, swing curves
and equal area criterion; HVDC transmission and FACTS concepts.
Control Systems: Principles of feedback; transfer function; block
diagrams; steady-state errors; Routh and Niquist techniques; Bode plots; root
loci; lag, lead and lead-lag compensation; state space model; state
transition matrix, controllability and observability.
Electrical and Electronic Measurements: Bridges and potentiometers;
PMMC, moving iron, dynamometer and induction type instruments; measurement of
voltage, current, power, energy and power factor; instrument transformers;
digital voltmeters and multimeters; phase, time and frequency measurement; Q-meters;
oscilloscopes; potentiometric recorders; error analysis.
Analog and Digital Electronics: Characteristics of diodes, BJT, FET;
amplifiers - biasing, equivalent circuit and frequency response; oscillators
and feedback amplifiers; operational amplifiers - characteristics and
applications; simple active filters; VCOs and timers; combinational and
sequential logic circuits; multiplexer; Schmitt trigger; multi-vibrators;
sample and hold circuits; A/D and D/A converters; 8-bit microprocessor
basics, architecture, programming and interfacing.
Power Electronics and Drives: Semiconductor power diodes, transistors,
thyristors, triacs, GTOs, MOSFETs and IGBTs - static characteristics and
principles of operation; triggering circuits; phase control rectifiers; bridge
converters - fully controlled and half controlled; principles of choppers and
inverters; basis concepts of adjustable speed dc and ac drives.
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